CN101515003B - Method for measuring surface charge density of materials - Google Patents
Method for measuring surface charge density of materials Download PDFInfo
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- CN101515003B CN101515003B CN2008101008202A CN200810100820A CN101515003B CN 101515003 B CN101515003 B CN 101515003B CN 2008101008202 A CN2008101008202 A CN 2008101008202A CN 200810100820 A CN200810100820 A CN 200810100820A CN 101515003 B CN101515003 B CN 101515003B
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Abstract
The invention provides a method for measuring the surface charge density of materials based on a conductive point of a scanning probe microscope, which comprises: a) scanning the surface appearance of a sample to be measured; b) measuring the change of a phase angle difference delta theta between actuating and alternating signals for driving the point to oscillate and actual oscillator signals ofthe point and a corresponding point bias Vt; c) according to a relation of the delta theta and the Vt, fitting the delta theta and the Vt obtained in step b) to obtain an index; and d) according to the index obtained in step c), searching the surface charge density corresponding to the index in a calibration curve based on the relation of the delta theta and the Vt, wherein the calibration curve is a relation curve of the surface charge density delta s of a standard sample and a coefficient a1. The method overcomes the difficulty of establishing a simple model for a geometrical shape of the point in the prior art, does not need considering the concrete geometrical shape of the point, makes the measurement simple and the operation easy, and has important significance for researching functions of nanodevices and nanostructures.
Description
Technical field
The invention belongs to the surface analysis technique field, be specifically related to the method that a kind of conductive pinpoint with scanning probe microscopy (Scanning Probe Microscope is called for short SPM) is measured surface charge density of materials.
Background technology
Can measure long-range electrostatic interaction power between needle point and the sample by the bias voltage that acts on conductive pinpoint or sample on the present market, can be used for surveying the surface potential of sample, the static state of ferroelectric material, dynamic property, electronic transport characteristic of single nanotube or the like.General conductive scanning probe microscope (Conductive Scanning Probe Microscope, abbreviation CSPM) needle point is an irregular pyramid needle point, shape and needle point-sample interval that the needle point charged particles produces electric field intensity and needle point have much relations, for a specific needle point, the electric field intensity of its generation is just only relevant with needle point-sample interval.Under the pattern of raising of CSPM, can be at nanometer range inner control sample to the spacing between the needle point, owing to the radius-of-curvature smaller (about 30nm) of needle point, so the sample in the nanometer range can be subjected to very strong electric field polarization under the needle point.In nano-scale, the electric density of quantitative detection sample surfaces has very important meaning for the device and the material physical chemistry performance of research nanoscale.The function of a lot of nano-devices or nanostructured is based on electric density in the nanoscale, or even the only a few electric charge, for example new explanation from mica surface and the interaction between the amino acid in, the electric density of mica surface plays important effect; In the coulomb latch up phenomenon, it is extremely important that the detection of single electron becomes.
In nano-scale, the electric density of setting up a kind of reliable method quantitative detection sample surfaces is the needs of nano science and technical development.Bibliographical information in the past, as M.J.Gordon and T.Baron at Physical Review B 72, in 165420 (2005) articles of delivering that are entitled as Amplitude-mode electrostatic force microscopy in UHV:Quantification of nanocrystal charge storage, provided the method for the conducting probe measuring samples surface charge density of a kind of amplitude-modulated use SPM.These class methods are taken the geometry of needle point into account, because the uncertainty and the complicacy of the geometric configuration of needle point, the more complicated that becomes based on the electric density of sample surfaces in the CSPM quantitative detection nanoscale, and need different needle point models for dissimilar needle points.Therefore, it is simple to need a kind of use, easy and simple to handle, is fit to the sample surface charge density measuring method of all kinds needle point geometric configuration.
Summary of the invention
Therefore, task of the present invention is to overcome the deficiencies in the prior art, thereby provides a kind of use simple, sample surface charge density measuring method easy and simple to handle.
The method of the measurement surface charge density of materials based on scanning probe microscope conductive pinpoint provided by the invention may further comprise the steps:
A) detected materials sample surfaces pattern is scanned;
B) under locking pin cusp height h, raise mode scanning, measure the excitation alternating signal and phasing degree difference Δ θ between the actual oscillator signal of needle point and the corresponding needle point bias voltage V that drive the needle point vibration along the track while scan of step a)
t
C) according to Δ θ and V
tRelation
Wherein, a
0, a
1And a
2Be all coefficient, Δ θ and V that step b) is obtained
tCarry out match, obtain the index index;
D) the index index that obtains according to step c) is based on Δ θ and V
tThe calibration curve of relation in search the pairing surface charge density of described index index, thereby obtain measured material sample surface charge density, wherein, the measuring method of described typical curve may further comprise the steps:
E) the standard model surface topography is scanned; The bias voltage of described standard model and the pass of its surface charge density are known;
F) under the needle point height h identical, respectively standard model is applied a plurality of bias voltages, measure the excitation alternating signal and phasing degree difference Δ θ between the actual oscillator signal of needle point and the corresponding needle point bias voltage V that drive the needle point vibration with step b)
t
G) according to Δ θ and V in the step (c)
tRelational expression Δ θ and V that step f) is obtained
tCarry out match, obtain the value of index index under the various criterion sample bias;
H) according to the known standard model bias voltage and the relation of surface charge density, obtain under the different bias voltages, the surface charge density of standard model, and, obtain the relation curve of surface charge density and described index index according to the result of step g), promptly obtain calibration curve.
In the said method, described Δ θ and V
tRelational expression in preferred a
1As described index index.
In the said method, described step b) is identical with the needlepoint form that step f) is used.
In the said method, the preferred conductor of described standard model, described conductor preferable alloy, for example: copper, iron, gold, silver, platinum, aluminium etc.
In the said method, the preferred spherical sample of described standard model.
Further, the diameter of described spherical sample is preferred 0.1 millimeter to 100 centimetres.
In the said method, use the phase-locking device of scanning probe microscope system to measure described phasing degree difference, perhaps when measuring described phasing degree difference, at first will drive the phasing degree zero setting of the excitation alternating signal of needle point vibration, directly measure the phasing degree of the actual oscillator signal of needle point then, promptly obtain described phasing degree difference.
The invention has the advantages that, for realizing based on the measurement of CSPM to sample surface charge density, set up simple distinct equation, described the relation of the variation of electrostatic interaction power that conductive pinpoint is subjected to and vibration phase and needle point bias voltage, sample polarization intensity; And on the basis of this relational expression, the relational expression between the electric density of clear and definite sample surfaces and the needle point voltage.The present invention is based on this relational expression, by the CSPM needle point material electric density to sample surfaces in nanometer range is measured, overcome prior art and the needle point geometric configuration set up the difficulty of naive model, needn't consider the concrete geometric configuration of needle point again, make and measure simply, easy and simple to handle, and also measuring process is to be based upon under the identical test condition, thereby avoided because the difference of measuring condition is introduced measured deviation.Function for research nano-device and nanostructured has very important meaning.
Description of drawings
Below, describe embodiments of the invention in conjunction with the accompanying drawings in detail, wherein:
Fig. 1 is main sweep and raises the scanning process synoptic diagram intermittence of raising pattern;
Fig. 2 is the variation of the tangent value of steel ball phase difference value under a series of sample bias with the needle point bias voltage;
Fig. 3 be the steel ball bias voltage with according to formula
The first power coefficient a that match obtains
1And quadratic power coefficient a
2Between relation;
Phase difference value and needle point bias voltage that Fig. 4 records from mica surface according to new explanation are according to formula
The first power coefficient a that match obtains
1Position in the steel ball calibration curve;
Fig. 5 is based on the process flow diagram of scanning probe microscopy measuring samples surface charge density.
Embodiment
The present invention is based on the method for CSPM measuring samples surface charge density, be described under a series of steel ball model bias effects, the phase change of CSPM conductive pinpoint vibration and the relation between the needle point bias voltage comprise the relation between sample surface charge density and the needle point bias voltage in its relational expression.In raising the scanning process of pattern, the acting force between needle point and the sample is mainly from three parts: the acting force that the electric capacity effect between needle point and the sample produces; Acting force between needle point charged particles and the sample surface charge density; The electric charge of sample surfaces and the sample surface charge acting force between the image charge of needle point.
Raising under the pattern, the total electrostatic force that acts on the micro-cantilever can be expressed as:
Wherein, C '
S-tipBe capacitor C between needle point-sample
S-tipIn the first order derivative of Z direction, the Z direction is the longitudinal direction of needle point, C
TipBe the isolated electric capacity of needle point, E
S-tipBe the electric field that sample surface charge produces, Q between sample-needle point
IsBe the image charge electric weight of sample surface charge in needle point, V
tBe the needle point bias voltage.
When F '＜＜during k, have
Wherein, Δ θ is the excitation alternating signal of driving needle point vibration and the phasing degree difference between the actual oscillator signal of needle point, and F ' is the derivative of F in the Z direction, and Q is the quality factor of needle point, and k is the elasticity coefficient of needle point, in conjunction with formula (1), can obtain,
Wherein, D
0Be a constant relevant with needlepoint form,
Be C
S-tipIn the second derivative of Z direction,
Be C
TipAt the first order derivative of Z direction, Q
sBe the sample surface charge number.
The electric field E that sample surface charge produces between sample-needle point
S-tipCan be expressed as:
E
s-tip＝ε
rδ
s＝k
0V
s (3)
k
0Be the constant relevant with the sample surfaces shape, ε
rBe dielectric constant of air, δ
sBe sample surface charge density, V
sBe sample surfaces voltage.
Therefore, phase difference value changes and can be expressed as:
Wherein, coefficient D
1For fixing sample surface charge density is a constant.By formula (3) and (4) as can be known, the first power coefficient and the V of the phase difference value tangent value tan (Δ θ) of needle point vibration and needle point bias relation formula
sRelation in direct ratio for the dielectric sample, according to formula (3), we can say that also tan (Δ θ) and sample surface charge density are in direct ratio.
In measuring method of the present invention, introduced a conducting sphere as standard model, because the relation between the electric density on conducting sphere surface and the conducting sphere bias voltage is clear and definite,
δ
g＝ε
rV
g/R
g (5)
Wherein, δ
gBe conducting sphere surface charge density, R
gBe the radius of conducting sphere, V
gBias voltage for conducting sphere.
Thereby under different conductor ball bias voltage, measure the tangent tan (Δ θ) of needle point vibration phase difference and the relation curve of needle point bias voltage,, obtain a series of at different conductor ball bias voltage V then according to formula (4) match
gDown, needle point bias voltage V
tThe coefficient of first power, can learn different conductor ball bias voltage V according to formula (5)
gPairing conducting sphere surface charge density δ
g,, obtain conducting sphere surface charge density δ as standard model by formula (4)
gWith needle point bias voltage V in the formula (4)
tThe relation curve of first power coefficient.,, under the situation of same needlepoint form and scanning height h, need only and obtained tan (Δ θ) and V as calibration curve with this relation curve by scanning
tRelation curve, just can learn V by match
tThe first power coefficient, as the index index, in calibration curve, search corresponding surface charge density with this first power coefficient according to this index index, be exactly the electric density on sample surface.
The present invention will be further explained and explanation below in conjunction with the drawings and specific embodiments.
Utilize commercial multiple mode scanning probe microscope in the present embodiment, at first introduce how to obtain calibration curve below, the steel ball that with the diameter is 5.01mm is as standard model, and the step of measuring calibration curve is as follows:
1) the steel ball surface pattern is carried out main sweep, in this main sweep process, feedback system is opened, and each bar sweep trace carries out shuttle-scanning one time, obtains the standard model surface topography;
2) needle point is raised to height 200nm, feedback system is closed, track while scan along step 1) repeats single pass, as shown in Figure 1, raise when scanning under the pattern this, needle point is applied the step bias voltage, respectively needle point and steel ball are applied needle point bias voltage and steel ball bias voltage by the bias voltage passage of SPM or by the lead that adds simultaneously, utilize the phase-locking device of multi-mode SPM, the excitation alternating signal of measurement driving needle point vibration and the phasing degree difference Δ θ between the actual oscillator signal of needle point are with needle point bias voltage V
tVariation;
3) according to formula
To Δ θ and V
tCarry out match, obtain V
tFirst power coefficient a
1At a plurality of steel ball bias voltage V
gRepeat this step 2 down) aforesaid operations, obtain corresponding a plurality of a
1As shown in Figure 2, provided as steel ball bias voltage V
gAt-10V when changing between+the 10V, tan (Δ θ) and V
tRelation curve, each bar curve can obtain a corresponding a by match
1Value;
4) simultaneously,, can obtain each steel ball bias voltage V according to formula (5)
gPairing sample surface charge density δ
g, make δ
gWith a
1Relation curve, promptly calibration curve as shown in Figure 3, has provided δ among the figure
g-a
1And δ
g-a
2Article two, curve, in Fig. 3, what the outer numeral of the transverse axis bracket of calibration curve provided is the steel ball bias value, and unit is a volt, and what the numeral in the bracket provided is the surface charge density of corresponding steel ball bias value, and unit is 10
10E/m
2, as seen from Figure 3, quadratic power coefficient a
2Very little, and change with the steel ball bias voltage hardly, those skilled in the art should understand, and this has proved that from the side what use above is spherical sample really.
Just introduced a kind of method for drafting of calibration curve above, except steel ball, can also copper, metal material such as iron, gold, silver, platinum, aluminium makes conducting sphere, preferred 0.1 millimeter to 100 centimetres of the diameter of conducting sphere, certainly, it will be appreciated by those skilled in the art that and also can use other suitable conductive materials to make conducting sphere, the diameter of conducting sphere depends primarily on the sample diameter that SPM can measure, and should not only limit to top preferable range.
After calibration curve has been arranged, just can measure testing sample, use in the present embodiment new explanation from mica as sample, measuring process as shown in Figure 5:
A) mica sample surfaces pattern to be measured is carried out main sweep, in the main sweep process, feedback system is opened;
B) raise mode scanning along the track while scan of step a), measure the excitation alternating signal and phasing degree difference Δ θ between the actual oscillator signal of needle point and the corresponding needle point bias voltage V that drive the needle point vibration
tWherein, scanning height h is identical with scanning height and the needle point of measurement during calibration curve with the used conductive pinpoint of scanning;
C) according to formula
Δ θ and V that step b) is obtained
tCarry out match, obtain a
1=14.3, wherein, a
0, a
1And a
2Be all coefficient;
D) a that obtains according to step c)
1, as shown in Figure 4, search in the calibration curve according to the steel ball acquisition in front, can learn that corresponding surface charge density is 1.6 * 10
7E/cm
2
In the process of above-mentioned measurement calibration curve and mica to be measured,, except the bias voltage passage that uses SPM, also can use the mode of external wire to apply for the Dc bias of steel ball and needle point; During measured phase angle difference DELTA θ, can also place zero degree in first phasing degree with pumping signal, directly measure the method at the phasing degree of the actual oscillator signal of needle point then, this moment, this phasing degree just equaled phasing degree difference Δ θ, in addition, needlepoint form in order to guarantee to measure testing sample used needlepoint form when measuring calibration curve is identical, and the best way is to use same needle point to measure, and does so farthest to reduce the error that the difference owing to needlepoint form causes.
The present invention derives
The process of relation is an exemplary explanation, and those skilled in the art can also select V according to top explanation and explanation
tThe quadratic power coefficient as the index index, but, from Fig. 3 also as can be seen because a
2Amplitude of variation very little, and approach zero, thus be not optimal selection, certainly, also fully can be under different approximate conditions, Δ θ and V voluntarily derive
tOther relational expressions, and select suitable index index according to the relational expression of deriving voluntarily, this is adequate to those skilled in the art.
It should be noted that at last above each accompanying drawing and embodiment only measure the technical scheme of surface charge density of materials in order to the conductive pinpoint that use scanning probe microscopy of the present invention is described, but unrestricted.Although the present invention is had been described in detail with reference to embodiment, those of ordinary skill in the art is to be understood that, technical scheme of the present invention is made amendment or is equal to replacement, do not break away from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.
Claims (9)
1. method based on the measurement surface charge density of materials of scanning probe microscope conductive pinpoint may further comprise the steps:
A) detected materials sample surfaces pattern is scanned;
B) under locking pin cusp height h, raise mode scanning, measure the excitation alternating signal and phasing degree difference Δ θ between the actual oscillator signal of needle point and the corresponding needle point bias voltage V that drive the needle point vibration along the track while scan of step a)
t
C) according to Δ θ and V
tRelation
A wherein
0, a
1And a
2Be all coefficient, Δ θ and V that step b) is obtained
tCarry out match, obtain the index index;
D) the index index that obtains according to step c) is based on Δ θ and V
tThe calibration curve of relation in search the pairing surface charge density of described index index, thereby obtain measured material sample surface charge density, wherein calibration curve obtains by following measuring method, this method may further comprise the steps:
E) the standard model surface topography is scanned; The bias voltage of described standard model and the pass of its surface charge density are known;
F) under the needle point height h identical, respectively standard model is applied a plurality of bias voltages, measure the excitation alternating signal and phasing degree difference Δ θ between the actual oscillator signal of needle point and the corresponding needle point bias voltage V that drive the needle point vibration with step b)
t
G) according to Δ θ and V in the step (c)
tRelational expression Δ θ and V that step f) is obtained
tCarry out match, obtain the value of index index under the various criterion sample bias;
H) according to the known standard model bias voltage and the relation of surface charge density, obtain under the different bias voltages, the surface charge density of standard model, and, obtain the relation curve of surface charge density and described index index according to the result of step g), promptly obtain calibration curve.
2. method according to claim 1 is characterized in that, described index index is a
1
3. method according to claim 1 is characterized in that, described step b) is identical with the needlepoint form that step f) is used.
4. method according to claim 1 is characterized in that described standard model is made by conductive material.
5. method according to claim 4 is characterized in that, described conductive material is copper, iron, gold, silver, platinum, aluminium.
6. method according to claim 1 is characterized in that the sphere that is shaped as of described standard model.
7. method according to claim 6 is characterized in that, the diameter of described spherical standard model is 0.1 millimeter to 100 centimetres.
8. method according to claim 1 is characterized in that, uses the phase-locking device of scanning probe microscope system to measure described phasing degree difference.
9. method according to claim 1, it is characterized in that, when measuring described phasing degree difference, at first will drive the phasing degree zero setting of the excitation alternating signal of needle point vibration, directly measure the phasing degree of the actual oscillator signal of needle point then, promptly obtain described phasing degree difference.
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Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102981023A (en) * | 2012-11-21 | 2013-03-20 | 哈尔滨理工大学 | Method for measuring surface potential by using electrostatic force microscope |
| CN104849497A (en) * | 2014-02-17 | 2015-08-19 | 国家纳米科学中心 | Device for measuring subsurface structure characteristic and micro-area wideband dielectric property |
| CN110824249B (en) * | 2019-11-19 | 2021-03-09 | 中国科学技术大学 | System and method for measuring transport property of nano device |
| CN112748153B (en) * | 2021-01-07 | 2023-01-10 | 中国人民大学 | Method and device for measuring electrical characteristics by amplitude modulation electrostatic force microscopy |
| CN113030602B (en) * | 2021-03-02 | 2022-10-21 | 北京纳米能源与系统研究所 | Method, device, equipment and medium for measuring electrical property of sample material |
| CN117590100B (en) * | 2023-11-27 | 2024-07-12 | 兰州理工大学 | Space charge measurement method and system based on non-contact vibration measurement |
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2008
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Patent Citations (4)
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| US5898106A (en) * | 1997-09-25 | 1999-04-27 | Digital Instruments, Inc. | Method and apparatus for obtaining improved vertical metrology measurements |
| US6449240B1 (en) * | 1999-03-29 | 2002-09-10 | Tdk Corporation | System, method and information medium for storing and reading information as a difference in a surface potential or a surface charge density |
| CN1672011A (en) * | 2002-07-04 | 2005-09-21 | 布里斯托尔大学 | Scanning probe microscope |
| CN1862308A (en) * | 2006-06-19 | 2006-11-15 | 中国科学院上海光学精密机械研究所 | modular scanning probe microscope |
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